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Length of Day

September 9, 2010

Summer vacations are over, and the days are getting shorter. A human reading that last sentence would understand the context and automatically recognize that what's really being said is that the period of daylight is getting shorter. A semi-intelligent machine would likely interpret the sentence as meaning that the sidereal rotation period of the Earth is decreasing from its usual value of 23 hours, 56 minutes and 4.100 seconds. Disaster movies aside, we all know that the period of Earth's rotation does not change. Well, actually it does, but just a little.[1]

Astronomers are very good at spotting stars out of place. Since the stars march from horizon to horizon because of Earth's rotation, astronomers are very sensitive to time, as well. Edmond Halley, discoverer of his eponymous comet, noticed variations in the length of day as early as 1695. Much of this variation is predictable, and it cycles annually. Out of the millisecond variation observed over the course of a year, the length of day increases during the northern hemisphere winter, and it decreases in the summer. The cause is a variation in the rotation rate of the Earth, which depends on how the mass of the Earth is distributed. Most of this variation is from the atmosphere, especially changes in the speed and direction of the jet stream. Temperature controls the jet stream, and the seasonal change in temperature therefore affects the length of day.[1]

Aside from this annual cycle, there are longer term variations caused by the Earth's molten core. Richard Gross did a thorough analysis of long term change in the length of day using historical astronomical records from 1832-1997.[2] To smooth the short term variations, he used a technique called Kalman filtering, much beloved by electrical engineers. A summary of his findings appears in the graph below.

Variation in the length of day, 1832-1997

Excess variation in the length of day, 1832-1997 (from Ref. 2).

What's more remarkable is recent research that shows that sunspots affect the length of day. A team of physicists from the Institut de Physique du Globe de Paris (France) examined data for the amplitude of the annual variation of the length-of-day over the period 1962 to 2009. The amplitude variation was modulated about 30% by the 11-yr cycle of sunspot number. As the number of sunspots goes up, the length of day goes down. There's a slight phase shift in these data, since the sunspot numbers lead the amplitude by about a year. The Paris team suspects that the mechanism is a sunspot alteration of winds on the Earth. Excess ultraviolet light from the Sun could heat the stratosphere, and that could affect the winds. Of course, much further work is needed, and since the effect is small and happens in an eleven year cycle, don't expect any quick results.

Image of the X-ray Sun near the maximum of the solar cycle.

Image of the X-ray Sun near the maximum of the solar cycle by the Yohkoh solar observatory (November 12, 1991, 07:33).


  1. All Days Are Not Created Equal, Jet Propulsion Laboratory Web Site, January 22, 2002.
  2. Richard S. Gross, "A combined length-of-day series spanning 1832-1997: LUNAR97," Physics of The Earth and Planetary Interiors, vol. 123, no. 1, (March 1, 2001), pp. 65-76.
  3. David Shiga, "Sunspots squeeze and stretch the day," New Scientist, issue 2775, August 27, 2010.
  4. J.-L. Le Mouël, E. Blanter, M. Shnirman, and V. Courtillot, "Solar forcing of the semi-annual variation of length-of-day," Geophysical Research Letters, Vol. 37, L15307 (August 13, 2010)

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Linked Keywords: daylight; Natural language understanding; sidereal rotation period; Earth; Disaster movies; rotation; Astronomers; Edmond Halley; Halley's comet; moment of inertia; jet stream; molten core; Kalman filtering; electrical engineers; sunspots; Institut de Physique du Globe de Paris; France; phase shift; ultraviolet; Sun; stratosphere; Yohkoh solar observatory.

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